{
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  "name": "",
  "signature": "sha256:30249a058876b3246e4fceec0244d1c83b76e5e3912d61b9b236c1db268e2d60"
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  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<small><i>This notebook was put together by [Jake Vanderplas](http://www.vanderplas.com) for PyCon 2015. Source and license info is on [GitHub](https://github.com/jakevdp/sklearn_pycon2015/).</i></small>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Supervised Learning In-Depth: Support Vector Machines"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Previously we introduced supervised machine learning.\n",
      "There are many supervised learning algorithms available; here we'll go into brief detail one of the most powerful and interesting methods: **Support Vector Machines (SVMs)**."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "from scipy import stats\n",
      "\n",
      "# use seaborn plotting defaults\n",
      "import seaborn as sns; sns.set()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Motivating Support Vector Machines"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Support Vector Machines (SVMs) are a powerful supervised learning algorithm used for **classification** or for **regression**. SVMs are a **discriminative** classifier: that is, they draw a boundary between clusters of data.\n",
      "\n",
      "Let's show a quick example of support vector classification. First we need to create a dataset:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sklearn.datasets.samples_generator import make_blobs\n",
      "X, y = make_blobs(n_samples=50, centers=2,\n",
      "                  random_state=0, cluster_std=0.60)\n",
      "plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='spring');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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C0sPIbJZFnUej6TRGr2+L/1AZB7hlv1/EA2/2pb6jfvHYynUrOfKWg+aJhoXJqpaje46Q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\n3ozvsZ49v89HHy3nsce+LF4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       "text": [
        "<matplotlib.figure.Figure at 0x109818128>"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "A discriminative classifier attempts to draw a line between the two sets of data. Immediately we see a problem: such a line is ill-posed! For example, we could come up with several possibilities which perfectly discriminate between the classes in this example:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "xfit = np.linspace(-1, 3.5)\n",
      "plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='spring')\n",
      "\n",
      "for m, b in [(1, 0.65), (0.5, 1.6), (-0.2, 2.9)]:\n",
      "    plt.plot(xfit, m * xfit + b, '-k')\n",
      "\n",
      "plt.xlim(-1, 3.5);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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iIeEkSUkJnD17msOHDzX7OSQZi3bj7OzMhEWT1Q5DCIvg7OzM3L8vIj8vH92V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\nCdwEGf8AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x109aba0f0>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "These are three *very* different separaters which perfectly discriminate between these samples. Depending on which you choose, a new data point will be classified almost entirely differently!\n",
      "\n",
      "How can we improve on this?"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Support Vector Machines: Maximizing the *Margin*\n",
      "\n",
      "Support vector machines are one way to address this.\n",
      "What support vector machined do is to not only draw a line, but consider a *region* about the line of some given width.  Here's an example of what it might look like:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "xfit = np.linspace(-1, 3.5)\n",
      "plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='spring')\n",
      "\n",
      "for m, b, d in [(1, 0.65, 0.33), (0.5, 1.6, 0.55), (-0.2, 2.9, 0.2)]:\n",
      "    yfit = m * xfit + b\n",
      "    plt.plot(xfit, yfit, '-k')\n",
      "    plt.fill_between(xfit, yfit - d, yfit + d, edgecolor='none', color='#AAAAAA', alpha=0.4)\n",
      "\n",
      "plt.xlim(-1, 3.5);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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mi1uwgCAiAcPYoNfrYTKFPh7McZzXalb8cRlcuvQZKisPoqGhHgAwe/ZsVFS8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\nf8nbdptBj806AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x109d23518>"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Notice here that if we want to maximize this width, the middle fit is clearly the best.\n",
      "This is the intuition of **support vector machines**, which optimize a linear discriminant model in conjunction with a **margin** representing the perpendicular distance between the datasets."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#### Fitting a Support Vector Machine\n",
      "\n",
      "Now we'll fit a Support Vector Machine Classifier to these points. While the mathematical details of the likelihood model are interesting, we'll let you read about those elsewhere. Instead, we'll just treat the scikit-learn algorithm as a black box which accomplishes the above task."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sklearn.svm import SVC # \"Support Vector Classifier\"\n",
      "clf = SVC(kernel='linear')\n",
      "clf.fit(X, y)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "SVC(C=1.0, cache_size=200, class_weight=None, coef0=0.0, degree=3, gamma=0.0,\n",
        "  kernel='linear', max_iter=-1, probability=False, random_state=None,\n",
        "  shrinking=True, tol=0.001, verbose=False)"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "To better visualize what's happening here, let's create a quick convenience function that will plot SVM decision boundaries for us:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def plot_svc_decision_function(clf, ax=None):\n",
      "    \"\"\"Plot the decision function for a 2D SVC\"\"\"\n",
      "    if ax is None:\n",
      "        ax = plt.gca()\n",
      "    x = np.linspace(plt.xlim()[0], plt.xlim()[1], 30)\n",
      "    y = np.linspace(plt.ylim()[0], plt.ylim()[1], 30)\n",
      "    Y, X = np.meshgrid(y, x)\n",
      "    P = np.zeros_like(X)\n",
      "    for i, xi in enumerate(x):\n",
      "        for j, yj in enumerate(y):\n",
      "            P[i, j] = clf.decision_function([xi, yj])\n",
      "    # plot the margins\n",
      "    ax.contour(X, Y, P, colors='k',\n",
      "               levels=[-1, 0, 1], alpha=0.5,\n",
      "               linestyles=['--', '-', '--'])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='spring')\n",
      "plot_svc_decision_function(clf);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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YZKUpSrFoNBpMmjRF1k7UkjDhEoWI6tIUi8WimLS2bNmIsrIy38Lw1Qn0W9/6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\nrkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10271a278>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Notice that the dashed lines touch a couple of the points: these points are the pivotal pieces of this fit, and are known as the *support vectors* (giving the algorithm its name).\n",
      "In scikit-learn, these are stored in the ``support_vectors_`` attribute of the classifier:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='spring')\n",
      "plot_svc_decision_function(clf)\n",
      "plt.scatter(clf.support_vectors_[:, 0], clf.support_vectors_[:, 1],\n",
      "            s=200, facecolors='none');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Nt9uluVKQ0+nkL3/5o6rdYDBoJlyz2UzXrt2wWCz+khSTyYTFop30TCYTL7zw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\nAWCA3wA44A7sUZGB/QAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10a395860>"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's use IPython's ``interact`` functionality to explore how the distribution of points affects the support vectors and the discriminative fit.\n",
      "(This is only available in IPython 2.0+, and will not work in a static view)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from IPython.html.widgets import interact\n",
      "\n",
      "def plot_svm(N=10):\n",
      "    X, y = make_blobs(n_samples=200, centers=2,\n",
      "                      random_state=0, cluster_std=0.60)\n",
      "    X = X[:N]\n",
      "    y = y[:N]\n",
      "    clf = SVC(kernel='linear')\n",
      "    clf.fit(X, y)\n",
      "    plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='spring')\n",
      "    plt.xlim(-1, 4)\n",
      "    plt.ylim(-1, 6)\n",
      "    plot_svc_decision_function(clf, plt.gca())\n",
      "    plt.scatter(clf.support_vectors_[:, 0], clf.support_vectors_[:, 1],\n",
      "                s=200, facecolors='none')\n",
      "    \n",
      "interact(plot_svm, N=[10, 200], kernel='linear');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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kJBoaGsnMzNww7t26kYWIN5ZlMTo6gmmeR2vNwsI8ABkZmRw+3IFSBtXVNRK4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\n73O5TuFynWJycpKkJAcuV+G+We5uYOA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       "text": [
        "<matplotlib.figure.Figure at 0x10a4c4da0>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Notice the unique thing about SVM is that only the support vectors matter: that is, if you moved any of the other points without letting them cross the decision boundaries, they would have no effect on the classification results!"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#### Going further: Kernel Methods\n",
      "\n",
      "Where SVM gets incredibly exciting is when it is used in conjunction with *kernels*.\n",
      "To motivate the need for kernels, let's look at some data which is not linearly separable:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sklearn.datasets.samples_generator import make_circles\n",
      "X, y = make_circles(100, factor=.1, noise=.1)\n",
      "\n",
      "clf = SVC(kernel='linear').fit(X, y)\n",
      "\n",
      "plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='spring')\n",
      "plot_svc_decision_function(clf);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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83M4jj4BOBzdvbuWTT04yZcpfffSJGpbdbsdsNvvNGub6YDmhus3SrhB+Png+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\nbkQAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10a3c4908>"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Clearly, no linear discrimination will ever separate these data.\n",
      "One way we can adjust this is to apply a **kernel**, which is some functional transformation of the input data.\n",
      "\n",
      "For example, one simple model we could use is a **radial basis function**"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "r = np.exp(-(X[:, 0] ** 2 + X[:, 1] ** 2))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "If we plot this along with our data, we can see the effect of it:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from mpl_toolkits import mplot3d\n",
      "\n",
      "def plot_3D(elev=30, azim=30):\n",
      "    ax = plt.subplot(projection='3d')\n",
      "    ax.scatter3D(X[:, 0], X[:, 1], r, c=y, s=50, cmap='spring')\n",
      "    ax.view_init(elev=elev, azim=azim)\n",
      "    ax.set_xlabel('x')\n",
      "    ax.set_ylabel('y')\n",
      "    ax.set_zlabel('r')\n",
      "\n",
      "interact(plot_3D, elev=[-90, 90], azip=(-180, 180));"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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YeCLvQZHOvFlBm0VH23jsI+8W5jXXbMH58/0xr09NTaGysiL8d3l5BaamJi38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NAAAN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\ngUAgiIAYTAKBQCAQRPD/gAA+0YHqsXcAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10a8e45c0>"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can see that with this additional dimension, the data becomes trivially linearly separable!\n",
      "This is a relatively simple kernel; SVM has a more sophisticated version of this kernel built-in to the process. This is accomplished by using ``kernel='rbf'``, short for *radial basis function*:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "clf = SVC(kernel='rbf')\n",
      "clf.fit(X, y)\n",
      "\n",
      "plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='spring')\n",
      "plot_svc_decision_function(clf)\n",
      "plt.scatter(clf.support_vectors_[:, 0], clf.support_vectors_[:, 1],\n",
      "            s=200, facecolors='none');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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dag3GPj4+xMSMJiZGQ3BwyKAajS6TyfDw8MTDw5NRoyzz0R/dC6+urqaqqpKq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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10a3c48d0>"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here there are effectively $N$ basis functions: one centered at each point! Through a clever mathematical trick, this computation proceeds very efficiently using the \"Kernel Trick\", without actually constructing the matrix of kernel evaluations.\n",
      "\n",
      "We'll leave SVMs for the time being and take a look at another classification algorithm: Random Forests."
     ]
    }
   ],
   "metadata": {}
  }
 ]
}